You can use this item in the store to allow members to send email invites. You can give permission to send invites by user role.
http://www.oxwall.org/store/item/426

Wilzer, it seems you haven't setup the Contact Importer plugin. Please check out the FAQ on how to setup it here: https://docs.oxwall.org/plugin-tuts:contact-importer.

Dear Taissa,
I left it out, maybe shouldn't have but wanted to make site member only and membership requires living in our community.  Thought import contacts would go through your computer's email address books and also maybe go through your Facebook Friends contacts and import these too.  Very few of these contacts would be eligible for membership in our community website.
Should I still set up contact importer?

BTW Oxwall is phenomenal

Wilzer, I apologize for delay in response. The Contact Importer plugin allows users to invite friends by sending personal email invitations or choosing from FB, Google+ contact lists. Users are always able to manage list of those whom they want to invite. For instance, here the screenshot on how to invite by email:

My members are nervous about sharing information, so having items from Google+ or Facebook  would not be desirable.

In the next update, could you simply add a check box in "Mail Notifications" that is visible to moderators to send email when Flag is set  set a category "Moderator"  with options below would really be nice.

Wilzer, please feel free to submit your idea at Oxwall uservoice to set it priority higher. We use our suggest board as one of the ways to show our product designers what features are the most essential. You can do it here:  http://oxwall.uservoice.com/forums/13756-ideas-for-oxwall.